Large off-highway sizes of pneumatic tires may be mounted on and demounted from drop-center wheels by using apparatus which applies a thrust slantingly to one side wall of the tire to drive its bead into the dropcenter of the wheel and to shift that side wall beyond center, drawing the bead out of round. Two contra-rotating bead deflectors then deflect the bead over the rim edge progressively, starting adjacent to the point of thrust application. Such apparatus is shown in U.S. Pat. Nos. 3,489,198 and 3,612,140. The thrust-applying cylinder is mounted on a turret rotatable about a horizontal axis, and is directed slantingly upward when its force is applied to the lower side wall of the tire, and slantingly downward when applied to the upper side wall. A shoe mounted rigidly on the end of the thrust cylinder is applied to the tire tread at one of the side walls, to exert the required force. A supplemental strut, used to change the angle of the cylinder, is pinned to its forward end, its aft end is secured to the turret at a vertical spacing from the thrust cylinder. Any load developed in the supplementary strut imposes undesirable bending stresses on the thrust-applying cylinder.